next up previous contents
Next: Chirp generation for test Up: GRASP Routines: Waveforms from Previous: The waveform   Contents

A note on the allowed frequency range

The frequency range of a signal calculated from black hole perturbation theory is bounded from above by the innermost stable circular orbit. This corresponds, by virtue of equation ([*]), to an orbital velocity of $v_{\rm max} =
\nicefrac{1}{\sqrt{6}}$. In practice there is also a lower bound. Since zero frequency would correspond to an infinite orbital radius we have to introduce a cutoff. In the present data files $v_{\rm min} \simeq
0.0395$. Figure [*] shows the allowed frequency range as a function of the total mass $M$.

Figure: Maximum and minimum orbital frequencies as a function of the total mass $M / M_\odot$ of the system.

Since $\dot{v}$ in equation ([*]) diverges at $v=v_{\rm max}$ calculating $v(t)$ at the upper limit is numerically difficult. However this is not a problem in the time domain, since the system spends very little time near $v =
v_{\rm min}$. An value of $f_{\rm max}$ inaccurate by several percent will typically not change the signal by even one wave cycle.


next up previous contents
Next: Chirp generation for test Up: GRASP Routines: Waveforms from Previous: The waveform   Contents
Bruce Allen 2000-11-19